50 g of ice at 0 °C is dropped into 200 g of water at 50 °C in an insulated container of negligible heat capacity. Take the specific heat of water as 4.2 J g⁻¹ K⁻¹ and the latent heat of fusion of ice as 336 J g⁻¹. The final temperature of the mixture is
Show the answer
Heat lost by water = heat to melt ice + heat to warm the melt: 200 × 4.2 × (50 − T) = 50 × 336 + 50 × 4.2 × T. So 42 000 − 840T = 16 800 + 210T, giving T = 24 °C.
- A.
40 °C ignores the latent heat needed to melt the ice.
- B.
0 °C would need the water to give up only enough heat to melt the ice, but it has 42 000 J available against 16 800 J needed.
- C.
30 °C does not satisfy the heat balance: heat lost would be 16 800 J but heat gained would be 23 100 J.
NCERT: Class 11 Physics, Chapter 10, Calorimetry and Change of state (latent heat)